The escalating atmospheric CO2 levels, which has been driving global warming, highlights the necessity to develop efficient CO2 capture technology, such as solid-based sorbents. Understanding the CO2 adsorption mechanism in these sorbents is important for their optimization, which, however, current semi-empirical models are not able to comprehensively demonstrate. In this paper, a diffusion-reaction model is proposed to elucidate the CO2 adsorption of a core-shell structured hydrogel sorbent. As the sorbent comprises a polyethylenimine hydrogel particle encapsulated by a silica shell, the model is developed by considering both physical diffusion and CO2-amine chemical reactions. As a result, the model describes the CO2 adsorption capacities of experimentally fabricated particles across diverse adsorption temperatures. Moreover, it unveils the CO2 adsorption process within the particle by displaying the evolution of amine-CO2 reaction rates, CO2 distribution, and amine consumption profiles. Notably, the model shows that the hydrogel core contributes to the primary diffusion resistance, a contrast to the less resistant silica shell. Overall, our diffusion-reaction model illuminates a fresh perspective on interpreting the CO2 adsorption mechanism of amine-based solid sorbents, from which insights can be gained for optimizing sorbent production in pursuit of carbon capture applications.